Preheat oven to 350F and line baking sheets with parchment paper or silicone mats.
Combine the flour, spices, baking soda and salt in a large bowl then whisk together and set aside.
Cream the butter and sugars together until light and fluffy. Add the eggs and vanilla extract and mix until combined. Scrape the bowl down then add the dry mixture and mix on low until almost combined.
Add the shredded carrot, oats, pecans, and coconut then mix on low until just combined.
Portion out heaping tablespoon balls of dough (35g), and place on lined cookie sheets about 2 inches apart. Bake for about 12 minutes or until the edges are golden.
While the cookies bake, cream the butter and cream cheese then add the powdered sugar and vanilla extract. Mix on high until well combined. You can add milk to adjust the consistency if desired.
Transfer a few tablespoons of the frosting into two small bowls and mix with orange and green food coloring. Transfer frosting to a piping bag fitted with a medium round tip or cut the tip off. If piping bunny faces choose a color for the fur and mix a tiny bit of pink buttercream for the ears.
Cover the cookies in butter cream then pipe carrots and bunny faces (see notes for decorating tips).